1. ## Sigma Notation Help

We've had a couple of classes on the topic with geometric sequences and arithmetic series as well. I've been having a propblem finding the values to use in the sum of the geometric sequence formula.
$
tn=\frac{ar^n-1}{r-1}
$

8
$
\sum(1/3)^(k-9)
$

k=4
Im having trouble getting the a and r values,is there any general rules you can use when looking for them in sigma notation

2. Originally Posted by nightrider456
We've had a couple of classes on the topic with geometric sequences and arithmetic series as well. I've been having a propblem finding the values to use in the sum of the geometric sequence formula.
$
tn=\frac{ar^n-1}{r-1}
$

8
$
\sum(1/3)^(k-9)
$

k=4
Im having trouble getting the a and r values,is there any general rules you can use when looking for them in sigma notation
I take it that this is actually

$\sum_{k = 4}^8 \left(\frac{1}{3}\right)^{k - 9}$.

Why not try writing out the first few terms?

$\sum_{k = 4}^8 \left(\frac{1}{3}\right)^{k - 9} = \left(\frac{1}{3}\right)^{-5} + \left(\frac{1}{3}\right)^{-4} + \left(\frac{1}{3}\right)^{-3} + \dots$

$= 243 + \frac{1}{3}\cdot 243 + \frac{1}{3}\cdot \frac{1}{3} \cdot 243 + \dots$.

Can you see what $a$ and $r$ are now?